Abstract
Over the past 20 years, much has been said, and then unsaid, about how risk capital should be allocated tactically inside financial institutions once strategic or regulatory capital is somehow determined. Although many of the techniques used for this purpose have proven their mettle within various institutions and contexts, the issue appears as unsettled as ever. This article takes a different tack and proposes a synthetic allocation regime combining risk and return, whereby value at risk and a measure of net operating income are the inputs to a reformulated Sharpe ratio driving the allocation. This first step is then combined with a weight-optimization step centered on the Chebyshev polynomial’s minimax property. The authors believe that resolving the internal allocation dilemma lies first in not focusing exclusively on either risk or return as the main driver but rather on their ratio, and second, in objectively and transparently avoiding the boundaries of the domain. Finally, although initial capital allocations should be made without regard for the size of the available market, ultimately one is compelled to pay homage to the prevailing macroeconomic reality. A detailed example of the approach and the mathematical rationale underlying Chebyshev optimization are included as separate appendices. TOPICS:VAR and use of alternative risk measures of trading risk, performance measurement, legal/regulatory/public policy, quantitative methods
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